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The equation of a parabola is given.

 

y=1/2x^2+6x+24

 

What is the equation of the directrix of the parabola?

 

Enter your answer in the box.

 May 24, 2018
 #1
avatar+118 
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Steps to finding the directrix given the equation of the parabola:
1) Find p-value
2) Find vertex
3) Sketch a diagram and label it (optional, but helpful)
steps 1 and 2 can be done in any order

 May 24, 2018
 #2
avatar+102320 
+2

y=1/2x^2+6x+24     factor out the 1/2

 

y  = (1/2) [ x^2 + 12x + 48  ] completet te square on x

 

y  = (1/2)  [ x^2  + 12 x  + 36  + 48 - 36 ]    factor the first three terms in the parenthses, simplify the rest

 

y =  (1/2)  [ ( x + 6)^2    + 12 ]      

 

y  =(1/2) ( x + 6)^2  + 6    

 

y - 6  =  (1/2)( x + 6)^2    multiply both sides by 2

 

2 ( y - 6)  = (x+ 6)^2

 

 

The vertex  is   ( --6, 6)

 

To find the directrix

 

4p  = 2

p = 2/4

p =  1/2

 

The parabola turns upward...so the  directrix   is   y  = 6  - 1/2   =  5.5

 

 

 

cool cool cool

 May 24, 2018

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